WASHINGTON — Even as officials from the Centers for Disease Control and Prevention are announcing that the epidemic of the H1N1 flu is no longer widespread in any state, no disease expert is willing to say there isn’t a third — or fourth — wave of the so-called swine flu in the country’s future.

Influenza transmission waxes and wanes, and outbreaks of novel pandemic strains occur in particularly unpredictable waves that depend on such variables as human behavior, atmospheric conditions and even competition from other microbes. That places them among the bigger mysteries of epidemiology, the science of disease outbreaks.

The Spanish flu of 1918 had four waves of greatly differing deadliness, spread over two years. The Asian flu of 1957, like the current H1N1 strain, had a late-spring and a fall wave — followed by a third in late winter of 1958. It then took a year off before peaking again in 1960. The Hong Kong flu of 1968 had more than a year hiatus between its two waves, with the second infecting nearly as many people as the first.

“We are not at all out of the woods because the virus continues to circulate, but the chances of a very large additional wave are very hard to predict,” said Anne Schuchat, who is leading the government’s response to the H1N1 pandemic at the CDC.

What explains the retreat of this flu since its peak in late October?

“That’s a great question, and it is still very much an open question,” said Katia Koelle, a biologist at Duke University who studies the dynamics of disease outbreaks.

Why doesn’t a flu outbreak last all winter, when the optimal conditions of low temperatures, low humidity and crowded living are present?

“It just doesn’t. It runs through a community and moves on,” said Walter Dowdle, who worked at CDC during the 1968 pandemic and is now an epidemiologist at the Task Force for Global Health in Decatur, Ga.

“Why do we have waves? I can’t find anybody who can tell me a biological explanation that makes sense,” said Michael Osterholm, director of the Center for Infectious Disease Research and Policy at the University of Minnesota.

At one level, the reason for H1N1’s waning is straightforward. People infected with the virus are passing it on to fewer people than they were last fall.

The growth and maintenance of a disease outbreak is a matter of simple arithmetic. If each person carrying a microbe passes it on to more than one person, the epidemic will spread. If each person passes it, on average, to fewer than one person — which means that many people don’t transmit it to anyone — then the epidemic will eventually burn out.

SPREAD IN SCHOOL

Flu viruses typically spread quickly among children, who gather in school and then pass the virus on to the rest of the population. The brief first wave last spring was most evident in schools, particularly in New York. The virus spread during the summer in places where children congregated, specifically camps. The second wave took off with the nationwide resumption of the school year in September.

“The main determinant of decline is vacation period, and the main determinant for the rise again is the aggregation of people for school terms,” said Roy Anderson, a professor of infectious-disease epidemiology at University College London.

One consequence of this is that when a lot of children get infected, recover and become immune, the entire epidemic slows down. “With this virus, once about half the children are infected … then you really can’t sustain transmission unless the infectivity goes up for some reason,” said Ira Longini, a disease modeler at the University of Washington.

That’s apparently what happened last fall and in the Asian flu of 1957, its eerily similar predecessor.

Visits to doctors’ offices for flu peaked in this pandemic in the week ending Oct. 24. In 1957, school absenteeism peaked in the last two weeks in October, depending on the city. (In both epidemics, the peaks occurred before there was any appreciable use of vaccine.)

So why did the virus start to ebb so early, and does that say anything about the likelihood of a third wave?

In 1957, the epidemic may have simply run out of children. A study of one of the first places hit by the 1957 virus — Tangipahoa Parish, in Louisiana — found that 60 percent of schoolchildren were infected in that fall wave. What fraction of schoolchildren are now immune to the H1N1 virus — either because they’ve had it, or have gotten the vaccine — isn’t known. But the CDC is trying to find out.

The Asian flu virus came back in February 1958, ultimately killing about 20,000 people (compared with 40,000 in the fall). Most of the deaths occurred among old people, who were spared in the fall for mysterious reasons — possibly because they had little contact with schoolchildren. Epidemiologists believe today’s elderly may be partly immune to the H1N1 virus because of exposure to a related virus that circulated more than 40 years ago. If so, an Asian-flu-like third wave is less likely.

CONDITIONS RIPE

What does seem clear is that environmental conditions for a flu outbreak are better now than they were last October.

A study published in December in the journal Public Library of Science Currents provided real-world support for numerous lab experiments showing that flu virus survives best in dry air.

A team of virologists and climate researchers, led by Jeffrey Shaman of Oregon State University, showed that over a period of 31 years seasonal flu outbreaks in the United States consistently started about three weeks after a marked decline in the humidity of the air. They used this observation to predict the timing of outbreaks in five states with different climates (Arizona, Florida, Illinois, New York and Washington), and the predictions were accurate.

The message is clear: When the air is dry, the virus spreads. Typically, winter air — both outdoors and in — is the driest of all seasons. The air is drier now than it was last fall, so the H1N1 virus should be spreading better now than it did in October. But it isn’t.

Of course, there may be other reasons for that, including the need for influenza virus to compete with other microbes for human noses and throats.

When a person is infected with one respiratory virus (such as rhinovirus, which causes colds), the chance of catching a different virus (such as flu) declines greatly. Part of the reason is that the first infection provokes what’s called “innate immunity” — a flood of interferon and other cellular hormones that defend the body in a general way without specifically targeting the invader. That protection can last weeks, breaking chains of transmission and slowing a flu epidemic.

A similar form of interference occurs between strains of flu, which is one of the reasons there has been almost no “seasonal flu” in recent months. The strains circulating last season and still occasionally found this season — H3N2, other forms of H1N1 and influenza B — have all been outcompeted by the upstart H1N1.

In fact, even if there isn’t a third wave, the new H1N1 may well spell the end of one or more of the families of flu virus that have been circulating for decades. That’s what has happened in previous pandemics, at least.

The H1N1 family arrived in 1918 with the Spanish flu. In the 1957 pandemic, the new virus was in the HN2 family; it drove all H1N1 strains to extinction. In 1968, the new virus was an H3N2. It spelled the end of the H2N2 family, which disappeared. H1N1 returned in 1977, apparently the result of an accidental release from a laboratory in Russia or China.

Like all pandemic strains, the novel H1N1 virus (or an immediate descendant of it) will eventually infect — but not necessarily sicken — nearly everybody on Earth who isn’t already immune to it through vaccination. It may take years. It could happen by unpredictable waves or slow percolation. But it is virtually inevitable.

“We’re going to have this virus for many decades to come,” said Longini, the University of Washington epidemic modeler. “And we don’t know what it’s going to do next.”

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